Answer:
The answer is indeed letter A. a portrait of his wife.
Explanation:
The poem "My Last Duchess", by Robert Browning, reveals the subject of the speaker's monologue in the very first line:
That’s my last Duchess painted on the wall,
Looking as if she were alive. I call
That piece a wonder, now; [...]
The probable speaker in the poem is the fifth Duke of Ferrara, Alfonso II d'Este. He married 14-year-old Lucrezia di Cosimo de' Medici, the duchess "painted on the wall". Rumor has it that she died at the age of 17 due to poisoning. Throughout poem, the Duke's arrogant and jealous nature can be noticed. His wife's beauty and happiness seemed to annoy him. The fact that her smiles were not directed only to him made him want to have them stop completely. He "gave commands" and the smiles did, in fact, stop.
Never to stoop. Oh, sir, she smiled, no doubt,
Whene’er I passed her; but who passed without
Much the same smile? This grew; I gave commands;
Then all smiles stopped together. [...]
